{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2023:QI2VLAIR7C272Z65I5Z6IDUENN","short_pith_number":"pith:QI2VLAIR","canonical_record":{"source":{"id":"2304.00395","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"cs.LG","submitted_at":"2023-04-01T21:53:29Z","cross_cats_sorted":["stat.ML"],"title_canon_sha256":"6274485f398351a0bbf2e7ac7317b982008a90e1731c5c6d6eabf4e46a162ab8","abstract_canon_sha256":"731dc2a7732d5884b5f3ce44a0658675a47c708bb70c8bbb7062612c599d7526"},"schema_version":"1.0"},"canonical_sha256":"8235558111f8b5fd67dd4773e40e846b7d2b8377a8314b64d9f2081e3950ab07","source":{"kind":"arxiv","id":"2304.00395","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2304.00395","created_at":"2026-07-05T06:42:20Z"},{"alias_kind":"arxiv_version","alias_value":"2304.00395v1","created_at":"2026-07-05T06:42:20Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2304.00395","created_at":"2026-07-05T06:42:20Z"},{"alias_kind":"pith_short_12","alias_value":"QI2VLAIR7C27","created_at":"2026-07-05T06:42:20Z"},{"alias_kind":"pith_short_16","alias_value":"QI2VLAIR7C272Z65","created_at":"2026-07-05T06:42:20Z"},{"alias_kind":"pith_short_8","alias_value":"QI2VLAIR","created_at":"2026-07-05T06:42:20Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2023:QI2VLAIR7C272Z65I5Z6IDUENN","target":"record","payload":{"canonical_record":{"source":{"id":"2304.00395","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"cs.LG","submitted_at":"2023-04-01T21:53:29Z","cross_cats_sorted":["stat.ML"],"title_canon_sha256":"6274485f398351a0bbf2e7ac7317b982008a90e1731c5c6d6eabf4e46a162ab8","abstract_canon_sha256":"731dc2a7732d5884b5f3ce44a0658675a47c708bb70c8bbb7062612c599d7526"},"schema_version":"1.0"},"canonical_sha256":"8235558111f8b5fd67dd4773e40e846b7d2b8377a8314b64d9f2081e3950ab07","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T06:42:20.510975Z","signature_b64":"WtK0+9XG/v2rXGIgGuuePEF6imS0yk4iBlUsYkrNDnpS2ZCjM6jE2diX4T94xHR5wNmZUBhNcK+N45Ks8Pv3Bw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"8235558111f8b5fd67dd4773e40e846b7d2b8377a8314b64d9f2081e3950ab07","last_reissued_at":"2026-07-05T06:42:20.510572Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T06:42:20.510572Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2304.00395","source_version":1,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-07-05T06:42:20Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"iWfMhgmgk/HhqVQK6u4YJyeigGMaMm9QRNdJ8qzOQO81fn72umKTabbeD/8cOYLFZ0OGwx2alTm0HiLiACo4BA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-04T09:42:25.714055Z"},"content_sha256":"d8d0910d204afc7fb465dd37a4cf4b222a764058b12ee9bd14e1ad735324794b","schema_version":"1.0","event_id":"sha256:d8d0910d204afc7fb465dd37a4cf4b222a764058b12ee9bd14e1ad735324794b"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2023:QI2VLAIR7C272Z65I5Z6IDUENN","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Towards Understanding the Mechanism of Contrastive Learning via Similarity Structure: A Theoretical Analysis","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["stat.ML"],"primary_cat":"cs.LG","authors_text":"Hiroki Waida, L\\'eo And\\'eol, Takafumi Kanamori, Takumi Nakagawa, Yuhui Zhang, Yuichiro Wada","submitted_at":"2023-04-01T21:53:29Z","abstract_excerpt":"Contrastive learning is an efficient approach to self-supervised representation learning. Although recent studies have made progress in the theoretical understanding of contrastive learning, the investigation of how to characterize the clusters of the learned representations is still limited. In this paper, we aim to elucidate the characterization from theoretical perspectives. To this end, we consider a kernel-based contrastive learning framework termed Kernel Contrastive Learning (KCL), where kernel functions play an important role when applying our theoretical results to other frameworks. W"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2304.00395","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2304.00395/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"},"verdict_id":null},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-07-05T06:42:20Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"kvnucCo0JEfWZArftFfSUkohUVD+LNYEcG6i0BYetw+WHfoNtqk+eRRD+kRWhQ3mePNfj8xZCd9R/9+qKpLMAQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-04T09:42:25.714576Z"},"content_sha256":"b2d408f2eec02c7a1c1ddf632f449d8d27c00a3af8f63067ab57d410c156f9ba","schema_version":"1.0","event_id":"sha256:b2d408f2eec02c7a1c1ddf632f449d8d27c00a3af8f63067ab57d410c156f9ba"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/QI2VLAIR7C272Z65I5Z6IDUENN/bundle.json","state_url":"https://pith.science/pith/QI2VLAIR7C272Z65I5Z6IDUENN/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/QI2VLAIR7C272Z65I5Z6IDUENN/bundle.json","status":"primary"}],"public_keys":[{"key_id":"pith-v1-2026-05","algorithm":"ed25519","format":"raw","public_key_b64":"stVStoiQhXFxp4s2pdzPNoqVNBMojDU/fJ2db5S3CbM=","public_key_hex":"b2d552b68890857171a78b36a5dccf368a953413288c353f7c9d9d6f94b709b3","fingerprint_sha256_b32_first128bits":"RVFV5Z2OI2J3ZUO7ERDEBCYNKS","fingerprint_sha256_hex":"8d4b5ee74e4693bcd1df2446408b0d54","rotates_at":null,"url":"https://pith.science/pith-signing-key.json","notes":"Pith uses this Ed25519 key to sign canonical record SHA-256 digests. Verify with: ed25519_verify(public_key, message=canonical_sha256_bytes, signature=base64decode(signature_b64))."}],"merge_version":"pith-open-graph-merge-v1","built_at":"2026-08-04T09:42:25Z","links":{"resolver":"https://pith.science/pith/QI2VLAIR7C272Z65I5Z6IDUENN","bundle":"https://pith.science/pith/QI2VLAIR7C272Z65I5Z6IDUENN/bundle.json","state":"https://pith.science/pith/QI2VLAIR7C272Z65I5Z6IDUENN/state.json","well_known_bundle":"https://pith.science/.well-known/pith/QI2VLAIR7C272Z65I5Z6IDUENN/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2023:QI2VLAIR7C272Z65I5Z6IDUENN","merge_version":"pith-open-graph-merge-v1","event_count":2,"valid_event_count":2,"invalid_event_count":0,"equivocation_count":0,"current":{"canonical_record":{"metadata":{"abstract_canon_sha256":"731dc2a7732d5884b5f3ce44a0658675a47c708bb70c8bbb7062612c599d7526","cross_cats_sorted":["stat.ML"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"cs.LG","submitted_at":"2023-04-01T21:53:29Z","title_canon_sha256":"6274485f398351a0bbf2e7ac7317b982008a90e1731c5c6d6eabf4e46a162ab8"},"schema_version":"1.0","source":{"id":"2304.00395","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2304.00395","created_at":"2026-07-05T06:42:20Z"},{"alias_kind":"arxiv_version","alias_value":"2304.00395v1","created_at":"2026-07-05T06:42:20Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2304.00395","created_at":"2026-07-05T06:42:20Z"},{"alias_kind":"pith_short_12","alias_value":"QI2VLAIR7C27","created_at":"2026-07-05T06:42:20Z"},{"alias_kind":"pith_short_16","alias_value":"QI2VLAIR7C272Z65","created_at":"2026-07-05T06:42:20Z"},{"alias_kind":"pith_short_8","alias_value":"QI2VLAIR","created_at":"2026-07-05T06:42:20Z"}],"graph_snapshots":[{"event_id":"sha256:b2d408f2eec02c7a1c1ddf632f449d8d27c00a3af8f63067ab57d410c156f9ba","target":"graph","created_at":"2026-07-05T06:42:20Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"graph_snapshot":{"author_claims":{"count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","strong_count":0},"builder_version":"pith-number-builder-2026-05-17-v1","claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/2304.00395/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"Contrastive learning is an efficient approach to self-supervised representation learning. Although recent studies have made progress in the theoretical understanding of contrastive learning, the investigation of how to characterize the clusters of the learned representations is still limited. In this paper, we aim to elucidate the characterization from theoretical perspectives. To this end, we consider a kernel-based contrastive learning framework termed Kernel Contrastive Learning (KCL), where kernel functions play an important role when applying our theoretical results to other frameworks. W","authors_text":"Hiroki Waida, L\\'eo And\\'eol, Takafumi Kanamori, Takumi Nakagawa, Yuhui Zhang, Yuichiro Wada","cross_cats":["stat.ML"],"headline":"","license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"cs.LG","submitted_at":"2023-04-01T21:53:29Z","title":"Towards Understanding the Mechanism of Contrastive Learning via Similarity Structure: A Theoretical Analysis"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2304.00395","kind":"arxiv","version":1},"verdict":{"created_at":null,"id":null,"model_set":{},"one_line_summary":"","pipeline_version":null,"pith_extraction_headline":"","strongest_claim":"","weakest_assumption":""}},"verdict_id":null}}],"author_attestations":[],"timestamp_anchors":[],"storage_attestations":[],"citation_signatures":[],"replication_records":[],"corrections":[],"mirror_hints":[],"record_created":{"event_id":"sha256:d8d0910d204afc7fb465dd37a4cf4b222a764058b12ee9bd14e1ad735324794b","target":"record","created_at":"2026-07-05T06:42:20Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"attestation_state":"computed","canonical_record":{"metadata":{"abstract_canon_sha256":"731dc2a7732d5884b5f3ce44a0658675a47c708bb70c8bbb7062612c599d7526","cross_cats_sorted":["stat.ML"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"cs.LG","submitted_at":"2023-04-01T21:53:29Z","title_canon_sha256":"6274485f398351a0bbf2e7ac7317b982008a90e1731c5c6d6eabf4e46a162ab8"},"schema_version":"1.0","source":{"id":"2304.00395","kind":"arxiv","version":1}},"canonical_sha256":"8235558111f8b5fd67dd4773e40e846b7d2b8377a8314b64d9f2081e3950ab07","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"8235558111f8b5fd67dd4773e40e846b7d2b8377a8314b64d9f2081e3950ab07","first_computed_at":"2026-07-05T06:42:20.510572Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T06:42:20.510572Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"WtK0+9XG/v2rXGIgGuuePEF6imS0yk4iBlUsYkrNDnpS2ZCjM6jE2diX4T94xHR5wNmZUBhNcK+N45Ks8Pv3Bw==","signature_status":"signed_v1","signed_at":"2026-07-05T06:42:20.510975Z","signed_message":"canonical_sha256_bytes"},"source_id":"2304.00395","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:d8d0910d204afc7fb465dd37a4cf4b222a764058b12ee9bd14e1ad735324794b","sha256:b2d408f2eec02c7a1c1ddf632f449d8d27c00a3af8f63067ab57d410c156f9ba"],"state_sha256":"1647143db83fba6b2d91dbcdd8dcc21ec80fdde716fdce0c357023b75a9608a6"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"zmSkaLRndjidCjwLs1yigXXR5tKl+TXBK/IZtU+55xMNbbOaRwaR1qipigA8f96uK2rnpF7LWkT+X5OYhSehDg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-04T09:42:25.720064Z","bundle_sha256":"9c5ef34467f07b3ce860459cf32b99771fb7da0a4d8aacc20c5c38c71ded3ae3"}}